图像复原是一个病态问题,一般需要通过规整化技术得到一个合适的解.规整化的难点在于抑制噪声的同时要保持图像的边缘等重要的图像信息.为了更有效地保持复原图像的边缘,提出了小波域边缘保持规整化泛函的一般形式,并给出了相应的求解方法.针对小波域图像复原方法可能产生的Gibbs效应,利用自然图像小波变换的水平（竖直）子带在水平（竖直）方向的连续性,通过额外的惩罚项加以解决.仿真实验结果说明了该方法的有效性.

Image restoration is an ill posed problem and must be regularized.Usually,the difficulty of regularization lies in avoiding the smoothing of edges while suppressing the noise.In order to preserve the edges of restored image effectively,a general wavelet based edge-preserving regularization scheme and the corresponding solving scheme are proposed.To get rid of the Gibbs effects of restoration algorithms in wavelet domain,the natural(image's) horizontal(vertical) continuity in horizontal(vertical) sub-band together with additioned punishment are employed.Experiments are presented which verified the theoretical results.